Abstract
Historically, the general problem of optimal design in optics has been concerned primarily with traditional imaging optical systems found, for example, in cameras, telescopes, and microscopes. In recent years the area has been broadened both by the need for improved, more efficient nonimaging optical systems, such as illuminators and backlights, and by the infusion of a new technology to fabricate diffractive phase structures. The design problem for nonimaging optical systems offers it own set of special challenges for mathematicians to such a degree that for many years engineers had to rely on empirical and simple analytical approaches. More recently, however, progress has been made in more rigorous mathematical approaches for the nonimaging problem, and these are described by Maes18 in another article in this Proceedings. This paper addresses the need for optimal design of imaging and diffractive optical systems from the engineering viewpoint and the author’s view of fruitful ground for applied mathematicians to explore.
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References
Abboud, T., and Nédélec, J., “Electromagnetic waves in an inhomogeneous medium, ” J. Math. Anal. Appl. Vol. 164, pp. 40 - 58 (1992).
Bao, G., “Finite elements approximation of time harmonic waves in periodic structures,” IMA Preprint Series # 1156, submitted.
Bao, G. and Dobson, D.C., “Diffractive optics in nonlinear media with periodic structure,” IMA Preprint Series #1124, submitted.
Born, M. and Wolf, E., Principles of Optics 6th Ed.(Permagon Press, NewYork, 1980 ).
Bruno, O.P. and Reitich, F., “Numerical solution of diffraction problems: a method of variation of boundaries,” J. Opt. Soc. Amer. A, to appear.
Cadilhac, M., “Rigorous vector theories of diffraction gratings,” in Progress in Optics Vol 21, E. Wolf, ed., ( North-Holland, New York, 1984 )
Cox, J.A. et al., “Diffraction efficiency of binary optical elements,” Proceedings SPIE Vol. 1211, pp. 116 - 24 (1990).
Cox, J.A., Fritz, B.S., and Werner, T., “Process error limitations on binary optics performnce,” Proceedings SPIE Vol. 1555, pp. 80 - 8, (1991).
Dobson, D.C., “Optimal design of periodic antireflective structures for the Helmholtz equation,” Euro. J. Appl. Math., Vol. 4, (1993) in press.
Dobson, D.C., “Phase reconstruction via nonlinear least-squares,” Inverse Prob-36 lems Vol. 8, pp. 541 - 57 (1992).
Dobson, D.C. and Cox, J.A., “Mathematical modeling for diffractive optics,” in Diffractive and Miniaturized Optics, SPIE Critical Reviews Vol CR47, S.H. Lee, ed. (1993).
Dobson, D. and Friedman, A., “The time-harmonic Maxwell equations in a doubly periodic structure,” J. Math. A.al. Appl. Vol. 166, pp. 507 - 28 (1992).
Farn, M.W., “New iterative algorithm for the design of phase-only gratings,” Computer and Optically Generated Holographic Optics, I.N. Cindrich and S. Lee, eds., Proceedings SPIE, Vol. 1555, pp. 34-42 (1991).
Gaylord, T.K. and Moharam M.G., “Analysis and Applications of Optical Diffraction by Gratings,” IEEE Proceedings Vol. 73 No. 5, pp. 894 - 937 (1985).
Gerchberg, R.W. and Saxton, W.O., “A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures.” Optik Vol$135 No. 2,, pp. 237 - 46, (1972).
Kirkpatrick, S., Gelatt, C.D. Jr.,Vecchi, M.P., “Optimization by Simulated Annealing,” Science Vol. 220, pp. 671 - 80 (1983).
Lee, S.H., ed., Diffractive and Miniaturized Optics, SPIE Critical Reviews, Vol. CR49 ( SPIE, Bellingham WA, 1994 ).
Maes, M., this Proceedings.
Petit, R., ed., Electromagnetic Theory of Gratings ( Springer-Verlag, Berlin, 1980 ).
Veldkamp, W.B. and Swanson, G.J., “Developments in fabrication of binary optical elements,” Proceedings SPIE Vol. 437, pp. 54 - 9 (1983).
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© 1994 Springer Fachmedien Wiesbaden
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Cox, J.A. (1994). Inverse and Optimal Design Problems for Imaging and Diffractive Optical Systems. In: Engl, H.W., McLaughlin, J. (eds) Proceedings of the Conference Inverse Problems and Optimal Design in Industry. European Consortium for Mathematics in Industry. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-96658-2_2
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DOI: https://doi.org/10.1007/978-3-322-96658-2_2
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